Experimenting with RSA digital signatures:

· Digital Signatures are built on top of Public Key Cryptography.

· The signer: The signature is generated using the signer’s private key.

· The verifier uses the signer’s public key to verify the signature and the original message.

Figure 1: Bob uses his own private key to generate a digital signature from a given message (originally Figure 5.2 from the book)

Q1: To generate a digital signature, what are the needed components?

Your answer?

Q2: In signing a document, is a ciphertext part of the output?

Your answer?

Figure 2: Alice (or anyone else) could use Bob’s public key to verify the message and the signature (originally Figure 5.3 from the book)

Q3: To verify a digital signature, what are the needed components?

Your answer?

Q4: What is the output of the signature verification process?

Your answer?

· Corrections of errors of codes in the book:

Figure 3: Correction of some errors of codes from the textbook

Exercises

Step 1: To generate an RSA key pair for Bob.

Review Figure 1 of Experimenting with Asymmetric Encryption and Decryption using RSA keys.

Step 2: Bob uses his private key to sign a message, and makes the message and the signature available for verification.

# script: BobSign.py

from cryptography.hazmat.primitives import hashes

from cryptography.hazmat.primitives.asymmetric import padding

from cryptography.hazmat.backends import default_backend

from cryptography.hazmat.primitives import serialization

import json

# Deserialization of Bob's private key

with open('private_key.pem', 'rb') as private_file:

loaded_private_key = serialization.load_pem_private_key(

private_file.read(),

password=None,

backend=default_backend()

)

# Use PSS padding when signing data;

# Use OAEP when encrypting data.

padding_config = padding.PSS(

mgf=padding.MGF1(hashes.SHA256()),

salt_length=padding.PSS.MAX_LENGTH)

message = b'message to be signed by Bob'

private_key = loaded_private_key

signature = private_key.sign(

message,

padding_config,

hashes.SHA256())

signed_msg = {

'message': list(message),

'signature': list(signature),

}

outbound_msg_to_alice = json.dumps(signed_msg)

# Save the signed message into a separate signed.dat file.

with open('signed.dat', 'wb') as signed_file:

signed_file.write(outbound_msg_to_alice.encode())

print("signed mesg and signature in 'signed.dat'.")

Figure 4: Signing a message

Step 3: Alice uses Bob’s public key to verify the signature and the message.

# script: BobVerify.py

from cryptography.hazmat.primitives import hashes

from cryptography.hazmat.primitives.asymmetric import padding

from cryptography.hazmat.backends import default_backend

from cryptography.hazmat.primitives import serialization

import hashlib

import json

from cryptography.exceptions import InvalidSignature

# Read the signed_mesg file

with open('signed.dat', 'rb') as signed_file:

inbound_msg_from_bob = signed_file.read()

signed_msg = json.loads(inbound_msg_from_bob)

message = bytes(signed_msg['message'])

signature = bytes(signed_msg['signature'])

# Deserialization of Bob's public key

with open('public_key.pem', 'rb') as public_file:

loaded_public_key = serialization.load_pem_public_key(

public_file.read(),

backend=default_backend()

)

padding_config = padding.PSS(

mgf=padding.MGF1(hashes.SHA256()),

salt_length=padding.PSS.MAX_LENGTH)

## NOTE: Errors of codes in the book

public_key = loaded_public_key

try:

public_key.verify( ## NOTE: Errors of codes in the book

signature,

message,

padding_config,

hashes.SHA256())

print('Trust message')

except InvalidSignature:

print('Do not trust message')

Figure 5: Signature Verification

Step 4: As shown in Figure 6, run both programs to verify the signature.

Figure 6: Run the BobSign.py and AliceVerify.py programs

Step 5: Save signed.dat to signed2.dat. Change the first byte in signed.dat from 109 to 111. Then run AliceVerify.py to see how it would work.

· Food for thought ...

Qa: Does digital signature provide confidentiality?

Qb: What security services are provided by using digital signatures?

Qc: How would you add confidentiality to the above programs?